Codebook feedback method and apparatus for multiple-antenna channel in mimo system

ABSTRACT

A codebook feedback method and apparatus for a multiple-antenna channel in a Multiple Input Multiple Output (MIMO) system are provided. In an embodiment, a method ( 20 ) includes: detecting ( 21 ) a downlink multiple-antenna channel; determining ( 22 ) a first codeword in a first level codebook corresponding to the rank of R, where any codeword in the first level codebook is four diagonal matrices, two same 2×C block matrices exist on a diagonal line, and C column vectors of the 2×C block matrix are selected from Q 1  discrete Fourier transform (DFT) beam vectors; feeding back ( 23 ) an index of the first codeword; determining ( 24 ) a second codeword in a second level codebook corresponding to the rank of R, where any codeword in the second level codebook is a 2C×R matrix, each column of the 2C×R matrix is formed of one C×1 beam selection vector and one C×1 beam selection vector including phase offset information; and feeding back ( 25 ) an index of the second codeword. The foregoing solution introduces an orthogonal DFT beam selection in two-level codebook index feedback, and therefore becomes more suitable for an MIMO application of a cross-polarized configuration of four downlink transmit antennas.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to the technology of mobilecommunications, and more specifically to a multiple user multiple inputmultiple output (MU MIMO) transmission technology.

2. Description of the Prior Art

In a Long Term Evolution (LTE) Release 10 (R10) system, when a basestation, that is, an evolved NodeB (eNB) adopts a setting of a 4-antennacross-polarized antenna array, because the Release 10 codebook is notprecise enough for such a setting of antennas, the effect of downlink MUMIMO is not as desirable as expected, which severely limits MU MIMOapplications.

SUMMARY OF THE INVENTION

One major objective is to provide a new technical solution for acodebook feedback in a MU-MIMO system and to overcome the foregoingdefect in the prior art.

An embodiment provides a method of feedback for a 4-antenna downlinkchannel in a Multiple Input Multiple Output (MIMO) system, whichincludes: detecting a downlink multiple-antenna channel; determining afirst codeword in a first level codebook corresponding to the rank of Raccording to a long-term broadband channel characteristic estimated froma result of the detection, where any codeword in the first levelcodebook is four diagonal matrices, two same 2×C block matrices exist ona diagonal line, and C column vectors of the 2×C block matrix areselected from Q₁ discrete Fourier transform (DFT) beam vectors; feedingback an index of the first codeword; determining a second codeword in asecond level codebook corresponding to the rank of R according to ashort-term channel characteristic estimated from the result of thedetection and the first codeword, where any codeword in the second levelcodebook is a 2C×R matrix, and each column of the 2C×R matrix is formedof one C×1 beam selection vector and one C×1 beam selection vectorincluding phase offset information; and feeding back an index of thesecond codeword.

An embodiment of the foregoing method further includes: determining arank of downlink transmission.

Another embodiment provides an apparatus of feedback for a 4-antennadownlink channel in a MIMO system, which includes: a detection module,configured to detect a downlink multiple-antenna channel; a firstdetermination module, configured to determine a first codeword in afirst level codebook corresponding to the rank of R according to along-term broadband channel characteristic estimated from a result ofthe detection, where any codeword in the first level codebook is fourdiagonal matrices, two same 2×C block matrices exist on a diagonal line,and C column vectors of the 2×C block matrix are selected from Q₁ DFTbeam vectors; a feedback module, configured to feed back an index of thefirst codeword; and a second determination module, configured todetermine a second codeword in a second level codebook corresponding tothe rank of R according to a short-term channel characteristic estimatedfrom the result of the detection and the first codeword, where anycodeword in the second level codebook is a 2C×R matrix, and each columnof the 2C×R matrix is formed of one C×1 beam selection vector and oneC×1 beam selection vector including phase offset information; where thefeedback module is further configured to feed back an index of thesecond codeword.

An embodiment of the foregoing apparatus further includes a thirddetermination module, configured to determine a rank of downlinktransmission.

An embodiment provides a user equipment, which includes the foregoingapparatus.

Yet another embodiment provides a method for use in a base stationhaving 4 transmit antennas in a MIMO system, which includes: receiving arank of downlink transmission, an index of a first codeword in a firstlevel codebook, and an index of a second codeword in a second levelcodebook fed back by a user equipment, where any codeword in the firstlevel codebook is four diagonal matrices, two same 2×C block matricesexist on a diagonal line, C column vectors of the 2×C block matrix areselected from Q₁ DFT beam vectors, any codeword in the second levelcodebook is a 2C×R matrix, and each column of the 2C×R matrix is formedof one C×1 beam selection vector and one C×1 beam selection vectorincluding phase offset information; and determining a downlink channelcharacteristic according to the rank, the index of the first codeword,and the index of the second codeword.

A further embodiment provides an apparatus for use in a base stationhaving 4 transmit antennas in a MIMO system, which includes: a receivingmodule, configured to receive a rank of downlink transmission, an indexof a first codeword in a first level codebook, and an index of a secondcodeword in a second level codebook fed back by a user equipment, whereany codeword in the first level codebook is four diagonal matrices, twosame 2×C block matrices exist on a diagonal line, C column vectors ofthe 2×C block matrix are selected from Q₁ DFT beam vectors, any codewordin the second level codebook is a 2C×R matrix, and each column of the2C×R matrix is formed of one C×1 beam selection vector and one C×1 beamselection vector including phase offset information; and a channelcharacteristic determination module, configured to determine a downlinkchannel characteristic according to the rank, the index of the firstcodeword, and the index of the second codeword.

An embodiment provides base station equipment, which includes theforegoing apparatus.

In some embodiments of the methods, apparatuses, and equipment, a columnvector of a codeword in the first level codebook includes DFT beamvectors with an equal stride and DFT beam vectors orthogonal to eachother, or includes DFT beam vectors with an equal stride but no DFT beamvectors orthogonal to each other.

In some other embodiments of the foregoing methods, apparatuses, andequipment, corresponding to the rank of 1, a column vector of anycodeword in the second level codebook is configured as selecting a sameor different DFT beam independently for each polarization, or configuredas selecting a same DFT beam for each polarization.

In yet some other embodiments of the foregoing methods, apparatuses, andequipment, corresponding to the rank of 2, a column vector of anycodeword in the second level codebook is configured as selecting a sameor different DFT beam independently for each polarization and selectinga same DFT beam for each layer, or configured as selecting a same ordifferent DFT beam for each layer independently and selecting a same DFTbeam for each polarization, or configured as selecting a same ordifferent DFT beam independently for each polarization and selecting asame or different DFT beam for each layer independently, or configuredas selecting a same DFT beam for each polarization and selecting a sameDFT beam for each layer.

In some further embodiments of the foregoing methods, apparatuses, andequipment, a first level codebook corresponding to the rank of 3 or 4 isa proper subset of a first level codebook corresponding to the rank of 1or 2.

In still some embodiments of the foregoing methods, apparatuses, andequipment, corresponding to the rank of 3 or 4, a column vector of the2×C block matrix includes DFT beam vectors orthogonal to each other, anda column vector of any codeword in the second level codebook isconfigured as selecting a same or different DFT beam independently foreach polarization, or configured as selecting a same DFT beam for eachpolarization.

The foregoing technical solutions introduce orthogonal DFT beamselection in two-level codebook index feedback, and therefore becomemore suitable for an MIMO application of a cross-polarized configurationof four downlink transmit antennas.

The technical features and advantages of the present invention areillustrated in brief above to make the following detailed illustrationof the present invention more comprehensible. Other features andadvantages of the present invention are described in the following,which constitute the subject of the claims of the present invention. Aperson skilled in the art shall understand that the disclosed conceptand embodiments may be easily used as a basis for modifying or designingother structures or processes for implementing an objective same as thatof the present invention. A person skilled in the art further shouldunderstand that such an equivalent structure does not depart from thespirit and scope of the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

With reference to the accompanying drawings, the following detailedillustration of the preferred embodiments pertaining to the presentinvention becomes more comprehensible. The present invention isillustrated exemplarily rather than to be limited by the accompanyingdrawings, and similar reference numerals in the accompanying drawingsrepresent similar components.

FIG. 1 shows an application scenario according to an embodiment of thepresent invention;

FIG. 2 is a flow chart of a method suitable for feedback for a 4-antennadownlink channel in a MIMO system according to an embodiment of thepresent invention;

FIG. 3 is a schematic structural view of an apparatus suitable forfeedback for a 4-antenna downlink channel in a MIMO system according toan embodiment of the present invention;

FIG. 4 is a flow chart of a method suitable for a base station having 4transmit antennas in a MIMO system according to an embodiment of thepresent invention; and

FIG. 5 is a schematic structural view of an apparatus suitable for abase station having 4 transmit antennas in a MIMO system according to anembodiment of the present invention.

DETAILED DESCRIPTION

The detailed illustration of the accompanying drawings is intended to bethe illustration of current preferred embodiments of the presentinvention, rather than to indicate a sole form to implement the presentinvention. It should be understood that the same or equivalent functionscan be accomplished by different embodiments that shall fall within thespirit and scope of the present invention.

A person skilled in the art shall understand that means and functionsdescribed here may be implemented by using software functions thatcombines a program-control microprocessor and a general-purposecomputer, and/or implemented by using an application-specific integratedcircuit (ASIC). It should be further understood that although thepresent invention is mainly illustrated in the forms of a method and anapparatus, the present invention may also be implemented as a computerprogram product and a system including a computer processor and a memoryconnected to the processor, where the memory is encoded by one or moreprograms that accomplish the functions disclosed herein.

FIG. 1 is a schematic view of an application scenario according to anembodiment of the present invention. The technical solution of thepresent invention is suitable for a MIMO system. As shown in FIG. 1, thescenario includes a base station equipment 1 and a user equipment 2. Thetechnical solution of the present invention is suitable for, forexample, without any limitation, feedback of a precoding matrix index(PMI) between the base station equipment 1 and the user equipment 2. Aperson skilled in the art shall understand that the base station or thebase station equipment stated herein is, for example, but is not limitedto, a NodeB or an evolved NodeB (eNB) in an LTE system or an LTE-Asystem. The technical solution of the present invention is also notlimited to an applicable LTE system or LTE-A system. The index feedbackhere adopts a two-level codebook solution, and a complete codeword Wcorresponds to a downlink channel characteristic, which may berepresented by the formula W=W₁*W₂. The first codeword W₁ is taken froma first level codebook B₁ and is configured to indicate a long-termbroadband channel characteristic. The second codeword W₂ is taken from asecond level codebook B₁ and is configured to indicate a short-termchannel characteristic. As the second codeword is obtained throughchannel detection on several corresponding sub-bands according to aservice demand of a user equipment, which is also often configured toindicate a channel characteristic of several corresponding sub-bands.The first codeword may be fed back by a long period, whereas the secondcodeword may be fed back by a short period.

FIG. 2 is a flow chart of a method suitable for feedback for a 4-antennadownlink channel in a MIMO system according to an embodiment of thepresent invention. As shown in FIG. 2, a method 20 includes Steps 21,22, 23, 24, and 25 execute by the user equipment 2.

In Step 21, the user equipment 2 detects a downlink multiple-antennachannel. For example, without any limitation, multiple antennas of thedownlink multiple-antenna channel detected by the user equipment 2 areall transmit antennas of the base station equipment 1.

In Step 22, the user equipment 2 determines a first codeword in a firstlevel codebook corresponding to the rank of R according to a long-termbroadband channel characteristic estimated from a result of thedetection, where any codeword in the first level codebook is fourdiagonal matrices, two same 2×C block matrices exist on a diagonal line,and C column vectors of the 2×C block matrix are selected from Q₁ DFTbeam vectors.

In Step 23, the user equipment 2 feeds back an index of the firstcodeword.

In Step 24, the user equipment 2 determines a second codeword in asecond level codebook corresponding to the rank of R according to ashort-term channel characteristic estimated from the result of thedetection and the first codeword, where any codeword in the second levelcodebook is a 2C×R matrix, and each column of the 2C×R matrix is formedof one C×1 beam selection vector and one C×1 beam selection vectorincluding phase offset information.

In Step 25, the user equipment 2 feeds back an index of the secondcodeword.

In some cases, the foregoing method 20 further includes Step 26, theuser equipment 2 determines a rank R of downlink transmission. In anenvironment of 4 downlink transmit antennas, R may be 1, 2, 3 or 4. Step26 is usually executed before Step 22.

FIG. 3 is a schematic structural view of an apparatus 30 suitable forfeedback for a 4-antenna downlink channel in a MIMO system according toan embodiment of the present invention. As shown in FIG. 3, theapparatus 30 includes a detection module 31, a first determinationmodule 32, a second determination module 33, and a feedback module 34.The apparatus 30 is usually configured in the user equipment 2.

The detection module 31 is configured to detect a downlinkmultiple-antenna channel.

The first determination module 32 is configured to determine a firstcodeword in a first level codebook corresponding to the rank of Raccording to a long-term broadband channel characteristic estimated froma result of the detection, where any codeword in the first levelcodebook is four diagonal matrices, two same 2×C block matrices exist ona diagonal line, and C column vectors of the 2×C block matrix areselected from Q₁ DFT beam vectors.

The feedback module 34 is configured to feed back an index of the firstcodeword.

The second determination module 33 is configured to determine a secondcodeword in a second level codebook corresponding to the rank of Raccording to a short-term channel characteristic estimated from theresult of the detection and the first codeword, where any codeword inthe second level codebook is a 2C×R matrix, and each column of the 2C×Rmatrix is formed of one C×1 beam selection vector and one C×1 beamselection vector including phase offset information.

The feedback module 34 is further configured to feed back an index ofthe second codeword.

In some cases, the foregoing apparatus 30 further includes a thirddetermination module 35, configured to determine a rank R of downlinktransmission. In an environment of 4 downlink transmit antennas, R maybe 1, 2, 3 or 4. The rank R is usually determined before the firstcodeword and the second codeword are determined.

FIG. 4 is a flow chart of a method suitable for a base station having 4transmit antennas in a MIMO system according to an embodiment of thepresent invention. As shown in FIG. 4, the method 40 includes steps 41and 42 executed by the base station equipment 1.

In Step 41, the base station equipment 1 receives a rank of downlinktransmission, an index of a first codeword in a first level codebook,and an index of a second codeword in a second level codebook fed back bya user equipment, where any codeword in the first level codebook is fourdiagonal matrices, two same 2×C block matrices exist on a diagonal line,C column vectors of the 2×C block matrix are selected from Q₁ DFT beamvectors, any codeword in the second level codebook is a 2C×R matrix, andeach column of the 2C×R matrix is formed of one C×1 beam selectionvector and one C×1 beam selection vector including phase offsetinformation.

In Step 42, the base station equipment 1 determines a downlink channelcharacteristic according to the rank, the index of the first codeword,and the index of the second codeword.

FIG. 5 is a schematic structural view of an apparatus 50 suitable for abase station having 4 transmit antennas in a MIMO system according to anembodiment of the present invention. As shown in FIG. 5, the apparatus50 includes a receiving module 51 and a channel characteristicdetermination module 52. The apparatus 50 is usually configured in thebase station equipment 1.

The receiving module 51 is configured to receive a rank of downlinktransmission, an index of a first codeword in a first level codebook,and an index of a second codeword in a second level codebook fed back bya user equipment, where any codeword in the first level codebook is fourdiagonal matrices, two same 2×C block matrices exist on a diagonal line,C column vectors of the 2×C block matrix are selected from Q₁ DFT beamvectors, any codeword in the second level codebook is a 2C×R matrix, andeach column of the 2C×R matrix is formed of one C×1 beam selectionvector and one C×1 beam selection vector including phase offsetinformation.

The channel characteristic determination module 52 is configured todetermine a downlink channel characteristic according to the rank, theindex of the first codeword, and the index of the second codeword.

In some embodiments, codebooks with the rank of 1 and the rank of 2adopt a same first level codebook B₁, where the total number N₁ ofcodewords in B₁ is 16, for which 4-bit encoding is adopted for indexfeedback. For the design of B₁, the following variables need to beconsidered, which include a size C of a beam set of each block matrix, abeam granularity Q₁, beam selection (α_(1,n), α_(2,n), . . . , α_(C,n)),and beam overlapping.

Several optional codebook solutions in consideration of differentcombinations are provided as follows:

In Embodiment 1.1, the size C of a beam set in a block matrix on adiagonal line in the first codeword W₁ is 4, the beam granularity Q₁ is16, and the beam selection is set to be (α_(1,n),α_(2,n), α_(3,n),α_(4,n))=(n,n+1,n+8,n+9), where n is a value between 0 and 15. The beamset includes adjacent and orthogonal DFT beams. The beam gap between theadjacent beams is 2π/16, and the gap between the orthogonal beams is π.Any codeword W₁ is represented as:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n \in \left\{ {0,1,\ldots \mspace{14mu},15} \right\}}$$X_{n} = {\begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\; \pi}{16}n} & ^{j\frac{2\; \pi}{16}{({n + 1})}} & ^{j\frac{2\; \pi}{16}{({n + 8})}} & ^{j\frac{2\; \pi}{16}{({n + 9})}}\end{bmatrix}.}$

Two DFT beams are overlapped in two adjacent codewords, and half of thecodewords in B₁ are repetitive. Such a first level codebook isredundant.

In Embodiment 1.2, the size C of a beam set in a block matrix on adiagonal line in the first codeword W₁ is 4, the beam granularity Q₁ is16, and the beam selection is set to be (α_(1,n),α_(2,n), α_(3,n),α_(4,n))=(n,n+1,n+2,n+3), where n is a value between 0 and 15. The beamset includes DFT beams with an equal stride, and the beam gap betweenadjacent beams is 2π/16. Any codeword W₁ is represented as:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n \in \left\{ {0,1,\ldots \mspace{14mu},15} \right\}}$$X_{n} = {\begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\; \pi}{16}n} & ^{j\frac{2\; \pi}{16}{({n + 1})}} & ^{j\frac{2\; \pi}{16}{({n + 2})}} & ^{j\frac{2\; \pi}{16}{({n + 3})}}\end{bmatrix}.}$

Three DFT beams are overlapped in two adjacent codewords, and codewordsin B1 are different from each other. Such a first level codebook is notredundant.

In Embodiment 1.3, the size C of a beam set in a block matrix on adiagonal line in the first codeword W₁ is 4, the beam granularity Q₁ is32, and the beam selection is set to be (α_(1,n),α_(2,n), α_(3,n),α_(4,n))=(n,n+1,n+16,n+17), where n is a value between 0 and 15. Thebeam set includes adjacent and orthogonal DFT beams. The beam gapbetween the adjacent beams is 2π/32, and the gap between the orthogonalbeams is π. Any codeword W₁ is represented as:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n \in \left\{ {0,1,\ldots \mspace{14mu},15} \right\}}$$X_{n} = {\begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\; \pi}{32}n} & ^{j\frac{2\; \pi}{32}{({n + 1})}} & ^{j\frac{2\; \pi}{32}{({n + 16})}} & ^{j\frac{2\; \pi}{32}{({n + 17})}}\end{bmatrix}.}$

Two DFT beams are overlapped in two adjacent codewords, and codewords inB1 are different from each other. Such a first level codebook is notredundant.

In Embodiment 1.4, the size C of a beam set in a block matrix on adiagonal line in the first codeword W₁ is 4, the beam granularity Q₁ is32, and the beam selection is set to be (α_(1,n),α_(2,n), α_(3,n),α_(4,n))=(2n,2n+1,2n+16,2n+17), where n is a value between 0 and 15. Thebeam set includes adjacent and orthogonal DFT beams. The beam gapbetween the adjacent beams is 2π/32, and the gap between the orthogonalbeams is π. Any codeword W₁ is represented as:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n \in \left\{ {0,1,\ldots \mspace{14mu},15} \right\}}$$X_{n} = {\begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\; \pi}{32}2n} & ^{j\frac{2\; \pi}{32}{({{2n} + 1})}} & ^{j\frac{2\; \pi}{32}{({{2n} + 16})}} & ^{j\frac{2\; \pi}{32}{({{2n} + 17})}}\end{bmatrix}.}$

No DFT beam is overlapped in two adjacent codewords, and half of thecodewords in B₁ are repetitive. Such a first level codebook isredundant.

In Embodiment 1.5, the size C of a beam set in a block matrix on adiagonal line in the first codeword W₁ is 4, the beam granularity Q₁ is32, and the beam selection is set to be (α_(1,n),α_(2,n), α_(3,n),α_(4,n))=(2n,2n+1,2n+2,2n+3), where n is a value between 0 and 15. Thebeam set includes DFT beams with an equal stride. The beam gap betweenthe adjacent beams is 2π/32. Any codeword W₁ is represented as:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n \in \left\{ {0,1,\ldots \mspace{14mu},15} \right\}}$$X_{n} = {\begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\; \pi}{32}2n} & ^{j\frac{2\; \pi}{32}{({{2n} + 1})}} & ^{j\frac{2\; \pi}{32}{({{2n} + 2})}} & ^{j\frac{2\; \pi}{32}{({{2n} + 3})}}\end{bmatrix}.}$

Two DFT beams are overlapped in two adjacent codewords, and codewords inB1 are different from each other. Such a first level codebook is notredundant.

In Embodiment 1.6, the size C of a beam set in a block matrix on adiagonal line in the first codeword W₁ is 2, the beam granularity Q₁ is16, and the beam selection is set to be (α_(1,n),α_(2,n))=(n,n+1), wheren is a value between 0 and 15. The beam set includes 2 adjacent DFTbeams, the beam gap between which is 2π/16. Any codeword W₁ isrepresented as:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n \in \left\{ {0,1,\ldots \mspace{14mu},15} \right\}}$$X_{n} = {\begin{bmatrix}1 & 1 \\^{j\frac{2\; \pi}{16}n} & ^{j\frac{2\; \pi}{16}{({n + 1})}}\end{bmatrix}.}$

Only one DFT beam is overlapped in two adjacent codewords, and codewordsin B1 are different from each other. Such a first level codebook is notredundant.

In Embodiment 1.7, the size C of a beam set in a block matrix on adiagonal line in the first codeword W₁ is 2, the beam granularity Q₁ is32, and the beam selection is set to be (α_(1,n),α_(2,n))=(n,n+16),where n is a value between 0 and 15. The beam set includes orthogonalDFT beams, and the beam gap is π. Any codeword W₁ is represented as:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n \in \left\{ {0,1,\ldots \mspace{14mu},15} \right\}}$$X_{n} = {\begin{bmatrix}1 & 1 \\^{j\frac{2\; \pi}{32}n} & ^{j\frac{2\; \pi}{32}{({n + 16})}}\end{bmatrix}.}$

No DFT beam is overlapped in each codeword, and codewords in B₁ aredifferent from each other. Such a first level codebook is not redundant.

In Embodiment 1.8, the size C of a beam set in a block matrix on adiagonal line in the first codeword W₁ is 2, the beam granularity Q₁ is16, and the beam selection is set to be (α_(1,n),α_(2,n))=(2n,2n+1),where n is a value between 0 and 15. The beam set includes adjacent DFTbeams, and the beam gap is 2π/32. Any codeword W₁ is represented as:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n \in \left\{ {0,1,\ldots \mspace{14mu},15} \right\}}$$X_{n} = {\begin{bmatrix}1 & 1 \\^{j\frac{2\; \pi}{32}2} & ^{j\frac{2\; \pi}{32}{({{2n} + 1})}}\end{bmatrix}.}$

No DFT beam is overlapped in each codeword, and codewords in B₁ aredifferent from each other. Such a first level codebook is not redundant.

In other embodiments, the size C of a beam set in a block matrix on adiagonal line in the first codeword W₁ is 2 or 4, and the beam setincludes a plurality of DFT beams with an equal stride or orthogonal toeach other. The orthogonal beams has a fixed gap of π; when the beamgranularity Q₁ is 32, the gap between the DFT beams with an equal stridemay be 2mπ/32 (where m is a random value between 1 and 15), and when thebeam granularity Q₁ is 16, the gap may be 2mπ/16 (where m is a randomvalue between 1 and 7).

For the second level codebook B₂ with the rank of 1 of the secondcodeword W₂, a beam selection method of a different polarization shouldbe considered according to the structure of the first level codebook.Several solutions of a second level codebook with the rank of 1 areprovided as follows:

In Embodiment 2.1, the size C of a beam set in a block matrix X_(n) is4, a same or different DFT beam is selected independently for eachpolarization, that is, y₁ and y₂ in any column of the codeword W₂ areeither same or different, and such a second level codebook is suitableto match the first level codebook B₁ that is redundant. The number N₂ ofcodewords in a second level codebook corresponding to the rank of 1 is16, and 4-bit is adopted for index feedback, where the beam selectionand the phase offset information have four options, respectively, forwhich 4-bit is adopted for index feedback, respectively. Any codeword W₂in the second level codebook B₂ is represented as:

$W_{2} = {{a_{1} \in C_{2}} = {{\left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{jy}_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{- y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\left\{ {\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{4}\end{bmatrix}} \right\}.}}}$

In Embodiment 2.2, the size C of a beam set in the block matrix X_(n) is4, a same DFT beam is selected for each polarization, that is, y₁ and y₂in any column of the second codeword W₂ are same, and such a secondlevel codebook is suitable to match the first level codebook B₁ that isnot redundant. The number N₂ of codewords in a second level codebookcorresponding to the rank of 1 is 16, and 4-bit is adopted for indexfeedback, where the beam selection and the phase offset information havefour options, respectively, for which 4-bit is adopted for indexfeedback, respectively. Any codeword W₂ in the second level codebook B₂is represented as:

$W_{2} = {{a_{1} \in C_{2}} = {{\left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{jy}_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{- y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\left\{ {\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{3} \\{\overset{\sim}{e}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{4} \\{\overset{\sim}{e}}_{4}\end{bmatrix}} \right\}.}}}$

In Embodiment 2.3, the size C of a beam set in a block matrix X_(n) is2, a same DFT beam is selected for each polarization, that is, y₁ and y₂in any column of the second codeword W₂ are same, and such a secondlevel codebook is suitable to match the first level codebook B₁ that isnot redundant. The number N₂ of codewords in a second level codebookcorresponding to the rank of 1 is 8, and 3-bit is adopted for indexfeedback, where the beam selection has two options for which 1-bit isadopted for index feedback, and the phase offset information has fouroptions for which 2-bit is adopted for index feedback. Any codeword W₂in the second level codebook B₂ is represented as:

$W_{2} = {{a_{1} \in C_{2}} = {{\left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{jy}_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{- y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\left\{ {\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix}} \right\}.}}}$

In Embodiment 2.4, the size C of a beam set in a block matrix X_(n) is2, a same or different DFT beam is selected independently for eachpolarization, that is, y₁ and y₂ in any column of the codeword W₂ areeither same or different. The number N₂ of codewords in a second levelcodebook corresponding to the rank of 1 is 16, and 4-bit is adopted forindex feedback, where the beam selection and the phase offsetinformation have four options, respectively, for which 4-bit is adoptedfor index feedback, respectively. Any codeword W₂ in the second levelcodebook B₂ is represented as:

$W_{2} = {{a_{1} \in C_{2}} = {{\left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{jy}_{2}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{- y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} \\{- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\left\{ {\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{1}\end{bmatrix}} \right\}.}}}$

For the second level codebook B₂ with the rank of 2 of the secondcodeword W₂, a beam selection method of a different polarization and adifferent layer should be considered according to the structure of thefirst level codebook. The solutions of the second level codebook withthe rank of 2 are provided as follows:

In Embodiment 3.1, the size C of a beam set in the block matrix X_(n) is4, a same or different DFT beam is selected independently for eachpolarization, a DFT beam is selected for each layer, and such a secondlevel codebook is suitable to match the first level codebook B₁ that isnot redundant. The number N₂ of the codewords in the second levelcodebook corresponding to the rank of 2 is 16, and 4-bit is adopted forindex feedback, where the beam selection has eight options, for which3-bit is adopted for index feedback, and the phase offset informationhas two options, for which 1-bit is adopted for index feedback. Anycodeword W₂ in the second level codebook B₂ is represented as:

$W_{2} = {{\left\lbrack {a_{1},a_{2}} \right\rbrack \in C_{2}} = {{\left\{ {{\frac{1}{2}\begin{bmatrix}y_{1} & y_{1} \\y_{2} & {- y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}y_{1} & y_{1} \\{jy}_{2} & {- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\left\{ {\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{4}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{3} \\{\overset{\sim}{e}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{4} \\{\overset{\sim}{e}}_{4}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{3} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{4} \\{\overset{\sim}{e}}_{2}\end{bmatrix}} \right\}.}}}$

In Embodiment 3.2, the size C of a beam set in a block matrix X_(n) is4, a same or different DFT beam is selected independently for eachlayer, a same DFT beam is selected for each polarization, and such asecond level codebook is suitable to match the first level codebook B₁that is not redundant. The number N₂ of the codewords in the secondlevel codebook corresponding to the rank of 2 is 16, and 4-bit isadopted for index feedback, where the beam selection has eight options,for which 3-bit is adopted for index feedback, and the phase offsetinformation has two options, for which 1-bit is adopted for indexfeedback. Any codeword W₂ in the second level codebook B₂ is representedas:

$W_{2} = {{\left\lbrack {a_{1},a_{2}} \right\rbrack \in C_{2}} = {{\left\{ {{\frac{1}{2}\begin{bmatrix}y_{1} & y_{2} \\y_{1} & {- y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}y_{1} & y_{2} \\{jy}_{1} & {- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\left\{ {\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{4}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{3} \\{\overset{\sim}{e}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{4} \\{\overset{\sim}{e}}_{4}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{3} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{4} \\{\overset{\sim}{e}}_{2}\end{bmatrix}} \right\}.}}}$

In Embodiment 3.3, the size C of a beam set in a block matrix X_(n) is4, a same or different DFT beam is selected independently for eachpolarization and layer, such a second level codebook is suitable tomatch the first level codebook B₁ that is redundant, and the blockmatrix X_(n) should include orthogonal DFT beams. The number N₂ of thecodewords in the second level codebook corresponding to the rank of 2 is16, and 4-bit is adopted for index feedback, where the beam selectionhas eight options, for which 3-bit is adopted for index feedback, andthe phase offset information has two options, for which 1-bit is adoptedfor index feedback. Any codeword W₂ in the second level codebook B₂ isrepresented as:

$W_{2} = {{\left\lbrack {a_{1},a_{2}} \right\rbrack \in C_{2}} = {{\left\{ {{\frac{1}{2}\begin{bmatrix}y_{1} & y_{3} \\y_{2} & {- y_{4}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}y_{1} & y_{3} \\{jy}_{2} & {- {jy}_{4}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} & y_{3} \\y_{2} & y_{4}\end{bmatrix}} \in {\begin{Bmatrix}{\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{1}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{2}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{3} & {\overset{\sim}{e}}_{3}\end{bmatrix},} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{4} & {\overset{\sim}{e}}_{4}\end{bmatrix} \\{\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3} \\{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4} \\{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3} \\{\overset{\sim}{e}}_{3} & {\overset{\sim}{e}}_{1}\end{bmatrix},} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4} \\{\overset{\sim}{e}}_{4} & {\overset{\sim}{e}}_{2}\end{bmatrix}\end{Bmatrix}.}}}$

In Embodiment 3.4, the size C of a beam set in a block matrix X_(n) is4, a same or different DFT beam is selected independently for eachpolarization, and a DFT beam is selected for each layer, and such asecond level codebook is suitable to match the first level codebook B₁that is redundant. The number N₂ of the codewords in the second levelcodebook corresponding to the rank of 2 is 8, and 3-bit is adopted forindex feedback, where the beam selection has four options, for which2-bit is adopted for index feedback, and the phase offset informationhas two options, for which 1-bit is adopted for index feedback. Anycodeword W₂ in the second level codebook B₂ is represented as:

$W_{2} = {{\left\lbrack {a_{1},a_{2}} \right\rbrack \in C_{2}} = {{\left\{ {{\frac{1}{2}\begin{bmatrix}y_{1} & y_{2} \\y_{1} & {- y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}y_{1} & y_{2} \\{jy}_{1} & {- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\left\{ {\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{4}\end{bmatrix}} \right\}.}}}$

In Embodiment 3.5, the size C of a beam set in a block matrix X_(n) is4, a same or different DFT beam is selected independently for eachlayer, a same DFT beam is selected for each polarization, and such asecond level codebook is suitable to match the first level codebook B₁that is redundant. The number N₂ of the codewords in the second levelcodebook corresponding to the rank of 2 is 8, and 3-bit is adopted forindex feedback, where the beam selection has four options, for which2-bit is adopted for index feedback, and the phase offset informationhas two options, for which 1-bit is adopted for index feedback. Anycodeword W₂ in the second level codebook B₂ is represented as:

$W_{2} = {{\left\lbrack {a_{1},a_{2}} \right\rbrack \in C_{2}} = {{\left\{ {{\frac{1}{2}\begin{bmatrix}y_{1} & y_{2} \\y_{1} & {- y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}y_{1} & y_{2} \\{jy}_{1} & {- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\left\{ {\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{4}\end{bmatrix}} \right\}.}}}$

In Embodiment 3.6, the size C of a beam set in a block matrix X_(n) is4, a same DFT beam is selected for each polarization, a same DFT beam isselected for each layer, and such a second level codebook is suitable tomatch the first level codebook B₁ that is not redundant. The number N₂of the codewords in the second level codebook corresponding to the rankof 2 is 8, and 3-bit is adopted for index feedback, where the beamselection has four options, for which 2-bit is adopted for indexfeedback, and the phase offset information has two options, for which1-bit is adopted for index feedback. Any codeword W₂ in the second levelcodebook B₂ is represented as:

$W_{2} = {{\left\lbrack {a_{1},a_{2}} \right\rbrack \in C_{2}} = {{\left\{ {{\frac{1}{2}\begin{bmatrix}y_{1} & y_{1} \\y_{2} & {- y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}y_{1} & y_{1} \\{jy}_{2} & {- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\left\{ {\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{3} \\{\overset{\sim}{e}}_{3}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{4} \\{\overset{\sim}{e}}_{4}\end{bmatrix}} \right\}.}}}$

In Embodiment 3.7, the size C of a beam set in a block matrix X_(n) is2, a same or different DFT beam is selected independently for eachpolarization, and a same or different DFT beam is selected independentlyfor each layer, such a second level codebook is suitable to match thefirst level codebook B₁ that is not redundant, and the block matrixX_(n) should include orthogonal DFT beams. The number N₂ of thecodewords in the second level codebook corresponding to the rank of 2 is16, and 4-bit is adopted for index feedback, where the beam selectionhas eight options, for which 3-bit is adopted for index feedback, andthe phase offset information has two options, for which 1-bit is adoptedfor index feedback. Any codeword W in the second level codebook B₂ isrepresented as:

$W_{2} = {{\left\lbrack {a_{1},a_{2}} \right\rbrack \in C_{2}} = {{\left\{ {{\frac{1}{2}\begin{bmatrix}y_{1} & y_{3} \\y_{2} & {- y_{4}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}y_{1} & y_{3} \\{jy}_{2} & {- {jy}_{4}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} & y_{3} \\y_{2} & y_{4}\end{bmatrix}} \in {\begin{Bmatrix}{\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{1}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{2}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{2}\end{bmatrix},} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{1}\end{bmatrix} \\{\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{2}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{1}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{1}\end{bmatrix},} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{2}\end{bmatrix}\end{Bmatrix}.}}}$

In Embodiment 3.8, the size C of a beam set in a block matrix X_(n) is2, a same or different DFT beam is selected independently for eachpolarization, and a same DFT beam is selected for each layer, and such asecond level codebook is suitable to match the first level codebook B₁that is not redundant. The number N₂ of the codewords in the secondlevel codebook corresponding to the rank of 2 is 8, and 3-bit is adoptedfor index feedback, where the beam selection has four options, for which2-bit is adopted for index feedback, and the phase offset informationhas two options, for which 1-bit is adopted for index feedback, Anycodeword W₂ in the second level codebook B₂ is represented as:

$W_{2} = {{\left\lbrack {a_{1},a_{2}} \right\rbrack \in C_{2}} = {{\left\{ {{\frac{1}{2}\begin{bmatrix}y_{1} & y_{1} \\y_{1} & {- y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}y_{1} & y_{1} \\{jy}_{1} & {- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\left\{ {\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{1}\end{bmatrix}} \right\}.}}}$

In Embodiment 3.9, the size C of a beam set in a block matrix X_(n) is2, a same or different DFT beam is selected independently for eachlayer, and a same DFT beam is selected for each polarization, and such asecond level codebook is suitable to match the first level codebook B₁that is not redundant. The number N₂ of the codewords in the secondlevel codebook corresponding to the rank of 2 is 8, and 3-bit is adoptedfor index feedback, where the beam selection has four options, for which2-bit is adopted for index feedback, and the phase offset informationhas two options, for which 1-bit is adopted for index feedback. Anycodeword W₂ in the second level codebook B₂ is represented as:

$W_{2} = {{\left\lbrack {a_{1},a_{2}} \right\rbrack \in C_{2}} = {{\left\{ {{\frac{1}{2}\begin{bmatrix}y_{1} & y_{2} \\y_{1} & {- y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}y_{1} & y_{2} \\{jy}_{1} & {- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\left\{ {\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{1}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{1} \\{\overset{\sim}{e}}_{2}\end{bmatrix},\begin{bmatrix}{\overset{\sim}{e}}_{2} \\{\overset{\sim}{e}}_{1}\end{bmatrix}} \right\}.}}}$

In some embodiments, codebooks with the rank of 3 and the rank of 4adopt the same first level codebook B₁, and several optional codebooksolutions are provided as follows:

In Embodiment 4.1, the first level codebook with the rank of 1 or therank of 2 is still a suitable first level codebook with the rank of 3 orthe rank of 4, which is not only suitable for the beam granularity Q₁ of16, but also is suitable for the beam granularity Q₁ of 32. 4-bit isstill adopted for index feedback.

In Embodiment 4.2, a suitable first level codebook with the rank of 3 orthe rank of 4 is a subset selected from a suitable first level codebookwith the rank of 1 or the rank of 2, for example, selected from thefirst level codebook in Embodiment 1.1. The size C of a beam set in ablock matrix on a diagonal line in the first codeword W₁ is 4, the beamgranularity Q₁ is 16, and the beam selection is set to be(α_(1,n),α_(2,n), α_(3,n), α_(4,n))=(n,n+1,n+8,n+9), where n is a valueamong 0, 2, 4, and 6. The beam set includes adjacent and orthogonal DFTbeams. The beam gap between the adjacent beams is 2π/16, and the gapbetween the orthogonal beams is π. No DFT beam is overlapped, and thefirst level codebook is not redundant. Any codeword W₁ is representedas:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n \in \left\{ {0,2,4,6} \right\}}$$X_{n} = {\begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{16}n} & ^{j\frac{2\pi}{16}{({n + 1})}} & ^{j\frac{2\pi}{16}{({n + 8})}} & ^{j\frac{2\pi}{16}{({n + 9})}}\end{bmatrix}.}$

In Embodiment 4.3, a suitable first level codebook with the rank of 3 orthe rank of 4 is a subset selected from a suitable first level codebookwith the rank of 1 or the rank of 2, for example, selected from thefirst level codebook in Embodiment 1.2. The size C of a beam set in ablock matrix on a diagonal line in the first codeword W₁ is 4, the beamgranularity Q₁ is 16, and the beam selection is set to be(α_(1,n),α_(2,n), α_(3,n), α_(4,n))=(n,n+1,n+2,n+3), and n is a valueamong 0, 4, 8, and 12. The beam set includes adjacent DFT beams, and thebeam gap between adjacent beams is 2π/16. No DFT beam is overlapped, andthe first level codebook is not redundant. Any codeword W₁ isrepresented as:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n \in \left\{ {0,4,8,12} \right\}}$$X_{n} = {\begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{16}n} & ^{j\frac{2\pi}{16}{({n + 1})}} & ^{j\frac{2\pi}{16}{({n + 2})}} & ^{j\frac{2\pi}{16}{({n + 3})}}\end{bmatrix}.}$

In Embodiment 4.4, a suitable first level codebook with the rank of 3 orthe rank of 4 is designed again and is different from the suitable firstlevel codebook with the rank of 1 or the rank of 2. The size C of a beamset in a block matrix on a diagonal line in the first codeword W₁ is 4,the beam granularity Q₁ is 8, and the beam selection is set to be(α_(1,n),α_(2,n), α_(3,n), α_(4,n))=(n,n+1,n+4,n+5), where n is a valuebetween 0 and 3. The beam set includes adjacent and orthogonal DFTbeams. The beam gap between the adjacent beams is 2π/8, and the gapbetween the orthogonal beams is 7π. Two DFT beams are overlapped in twoadjacent codewords, and no repetitive codeword exists in B₁. Such afirst level codebook is not redundant. Any codeword W₁ is representedas:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{n \in \left\{ {0,1,2,3} \right\}}$$X_{n} = {\begin{bmatrix}1 & 1 & 1 & 1 \\^{j\frac{2\pi}{8}n} & ^{j\frac{2\pi}{8}{({n + 1})}} & ^{j\frac{2\pi}{8}{({n + 4})}} & ^{j\frac{2\pi}{8}{({n + 5})}}\end{bmatrix}.}$

Embodiment 5.1 is a design corresponding to the second level codebook B₂with the rank of 3. The size C of a beam set in a block matrix X_(n) is4, and a same or different DFT beam is selected independently for eachpolarization. The block matrix X_(n) should include orthogonal DFTbeams. The number N₂ of the codewords in the second level codebook is16, and 4-bit is adopted for index feedback, where the beam selectionhas 16 options, for which 4-bit is adopted for feedback, and the phaseoffset information only has one option. Any codeword W₂ in the secondlevel codebook B₂ is represented as:

$W_{2} = {{\left\lbrack {a_{1},a_{2},a_{3}} \right\rbrack \in C_{2}} = {{\left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} & y_{3} \\y_{2} & {- y_{4}}\end{bmatrix}} \right\} \begin{bmatrix}y_{1} & y_{3} \\y_{2} & y_{4}\end{bmatrix}} \in {\begin{bmatrix}{\begin{bmatrix}{\overset{\sim}{e}}_{1} & \begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} \\{\overset{\sim}{e}}_{1} & \begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{2} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} \\{\overset{\sim}{e}}_{2} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix}\end{bmatrix},} \\{\begin{bmatrix}{\overset{\sim}{e}}_{3} & \begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} \\{\overset{\sim}{e}}_{3} & \begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{4} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} \\{\overset{\sim}{e}}_{4} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix}\end{bmatrix},} \\{\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{1\;} & {\overset{\sim}{e}}_{3}\end{bmatrix} & {\overset{\sim}{e}}_{3} \\\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} & {\overset{\sim}{e}}_{3}\end{bmatrix},} & {\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} & {\overset{\sim}{e}}_{4} \\\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} & {\overset{\sim}{e}}_{4}\end{bmatrix},} \\{\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{3} & {\overset{\sim}{e}}_{1}\end{bmatrix} & {\overset{\sim}{e}}_{1} \\\begin{bmatrix}{\overset{\sim}{e}}_{3} & {\overset{\sim}{e}}_{1}\end{bmatrix} & {\overset{\sim}{e}}_{1}\end{bmatrix},} & {\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{4} & {\overset{\sim}{e}}_{2}\end{bmatrix} & {\overset{\sim}{e}}_{2} \\\begin{bmatrix}{\overset{\sim}{e}}_{4} & {\overset{\sim}{e}}_{2}\end{bmatrix} & {\overset{\sim}{e}}_{2}\end{bmatrix},} \\{\begin{bmatrix}{\overset{\sim}{e}}_{1} & \begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} \\{\overset{\sim}{e}}_{3} & \begin{bmatrix}{\overset{\sim}{e}}_{3} & {\overset{\sim}{e}}_{1}\end{bmatrix}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{2} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} \\{\overset{\sim}{e}}_{4} & \begin{bmatrix}{\overset{\sim}{e}}_{4} & {\overset{\sim}{e}}_{2}\end{bmatrix}\end{bmatrix},} \\{\begin{bmatrix}{\overset{\sim}{e}}_{3} & \begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} \\{\overset{\sim}{e}}_{1} & \begin{bmatrix}{\overset{\sim}{e}}_{3} & {\overset{\sim}{e}}_{1}\end{bmatrix}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{4} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} \\{\overset{\sim}{e}}_{2} & \begin{bmatrix}{\overset{\sim}{e}}_{4} & {\overset{\sim}{e}}_{2}\end{bmatrix}\end{bmatrix},} \\{\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{1\;} & {\overset{\sim}{e}}_{3}\end{bmatrix} & {\overset{\sim}{e}}_{3} \\\begin{bmatrix}{\overset{\sim}{e}}_{3} & {\overset{\sim}{e}}_{1}\end{bmatrix} & {\overset{\sim}{e}}_{1}\end{bmatrix},} & {\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{2\;} & {\overset{\sim}{e}}_{4}\end{bmatrix} & {\overset{\sim}{e}}_{4} \\\begin{bmatrix}{\overset{\sim}{e}}_{4} & {\overset{\sim}{e}}_{2}\end{bmatrix} & {\overset{\sim}{e}}_{2}\end{bmatrix},} \\{\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{3\;} & {\overset{\sim}{e}}_{1}\end{bmatrix} & {\overset{\sim}{e}}_{1} \\\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} & {\overset{\sim}{e}}_{3}\end{bmatrix},} & \begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{4\;} & {\overset{\sim}{e}}_{2}\end{bmatrix} & {\overset{\sim}{e}}_{2} \\\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} & {\overset{\sim}{e}}_{4}\end{bmatrix}\end{bmatrix}.}}}$

Embodiment 5.2 is a design corresponding to the second level codebook B₂with the rank of 3. The size C of a beam set in a block matrix X_(n) is4, and a same DFT beam is selected for each polarization. The blockmatrix X_(n) should include orthogonal DFT beams. The number N₂ of thecodewords in the second level codebook is 8, and 3-bit is adopted forindex feedback, where the beam selection has eight options, for which3-bit is adopted for feedback, and the phase offset information only hasone option. Any codeword W₂ in the second level codebook B₂ isrepresented as:

$W_{2} = {{\left\lbrack {a_{1},a_{2},a_{3},a_{4}} \right\rbrack \in C_{2}} = {{\left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}y_{1} & y_{3} \\y_{2} & {- y_{4}}\end{bmatrix}} \right\} \begin{bmatrix}y_{1} & y_{3} \\y_{2} & y_{4}\end{bmatrix}} \in {\begin{Bmatrix}{\begin{bmatrix}{\overset{\sim}{e}}_{1} & \begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} \\{\overset{\sim}{e}}_{1} & \begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{2} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} \\{\overset{\sim}{e}}_{2} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix}\end{bmatrix},} \\{\begin{bmatrix}{\overset{\sim}{e}}_{3} & \begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} \\{\overset{\sim}{e}}_{3} & \begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix}\end{bmatrix},} & {\begin{bmatrix}{\overset{\sim}{e}}_{4} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} \\{\overset{\sim}{e}}_{4} & \begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix}\end{bmatrix},} \\{\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} & {\overset{\sim}{e}}_{3} \\\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} & {\overset{\sim}{e}}_{3}\end{bmatrix},} & {\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} & {\overset{\sim}{e}}_{4} \\\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} & {\overset{\sim}{e}}_{4}\end{bmatrix},} \\{\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{3} & {\overset{\sim}{e}}_{1}\end{bmatrix} & {\overset{\sim}{e}}_{1} \\\begin{bmatrix}{\overset{\sim}{e}}_{3} & {\overset{\sim}{e}}_{1}\end{bmatrix} & {\overset{\sim}{e}}_{1}\end{bmatrix},} & \begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{4} & {\overset{\sim}{e}}_{2}\end{bmatrix} & {\overset{\sim}{e}}_{2} \\\begin{bmatrix}{\overset{\sim}{e}}_{4} & {\overset{\sim}{e}}_{2}\end{bmatrix} & {\overset{\sim}{e}}_{2}\end{bmatrix}\end{Bmatrix}.}}}$

Embodiment 6.1 corresponds to the design of a second level codebook B₂with the rank of 4. The size C of a beam set in a block matrix X_(n) is4, and a same or different DFT beam is selected independently for eachpolarization. The block matrix X_(n) should include orthogonal DFTbeams. The number N₂ of codewords in the second level codebook is 8, and3-bit is adopted for index feedback, where the beam selection has fouroptions, for which 2-bit is adopted for feedback, and the phase offsetinformation has two options, for which 1-bit is adopted for feedback.Any codeword W₂ in the second level codebook B₂ is represented as:

$W_{2} = {{\left\lbrack {a_{1},a_{2},a_{3},a_{4}} \right\rbrack \in C_{2}} = {{\left\{ {{\frac{1}{2}\begin{bmatrix}y_{1} & y_{1} \\y_{2} & {- y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}y_{1} & y_{1} \\{jy}_{2} & {- {jy}_{2}}\end{bmatrix}}} \right\} \begin{bmatrix}y_{1} \\y_{2}\end{bmatrix}} \in {\begin{Bmatrix}{\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} \\\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix}\end{bmatrix},} & {\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} \\\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix}\end{bmatrix},} & {\begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{1} & {\overset{\sim}{e}}_{3}\end{bmatrix} \\\begin{bmatrix}{\overset{\sim}{e}}_{3} & {\overset{\sim}{e}}_{1}\end{bmatrix}\end{bmatrix},} & \begin{bmatrix}\begin{bmatrix}{\overset{\sim}{e}}_{2} & {\overset{\sim}{e}}_{4}\end{bmatrix} \\\begin{bmatrix}{\overset{\sim}{e}}_{4} & {\overset{\sim}{e}}_{2}\end{bmatrix}\end{bmatrix}\end{Bmatrix}.}}}$

The foregoing embodiments are all exemplary rather than limitative. Theforegoing technical solutions introduce orthogonal DFT beam selection intwo-level codebook index feedback, and therefore become more suitablefor an MIMO application of a cross-polarized configuration of fourdownlink transmit antennas. Definitely, the foregoing technicalsolutions are also suitable for an MIMO application of a linear arrayconfiguration of transmit antennas.

A person skilled in the art shall understand that the function of any ofthe foregoing modules can be executed by a plurality of entity modulesor functional modules, and the functions of the foregoing modules mayalso be integrated in one entity module or functional module forexecution.

Although different embodiments of the present invention are illustratedand described, the present invention is not limited to theseembodiments. Ordinal numbers such as “first” and “second” only have theeffect for differentiation rather than to indicate any particular orderor connection relationship between corresponding components. A technicalfeature that only appears in some claims or embodiments does not meanthat it cannot be combined with other features in other claims orembodiments to implement a new, beneficial technical solution. Variousmodifications, changes, variations, replacements, and equivalents areobvious to a person skilled in the art without departing from the spiritand scope of the present invention as described in the claims.

1. A method of feedback for a 4-antenna downlink channel in a MultipleInput Multiple Output (MIMO) system, comprising: detecting a downlinkmultiple-antenna channel; determining a first codeword in a first levelcodebook corresponding to the rank of R according to a long-termbroadband channel characteristic estimated from a result of thedetection, wherein any codeword in the first level codebook is fourdiagonal matrices, two same 2×C block matrices exist on a diagonal line,and C column vectors of the 2×C block matrix are selected from Q₁discrete Fourier transform (DFT) beam vectors; feeding back an index ofthe first codeword; determining a second codeword in a second levelcodebook corresponding to the rank of R according to a short-termchannel characteristic estimated from the result of the detection andthe first codeword, wherein any codeword in the second level codebook isa 2C×R matrix, and each column of the 2C×R matrix is formed of one C×1beam selection vector and one C×1 beam selection vector comprising phaseoffset information; and feeding back an index of the second codeword.2.-7. (canceled)
 8. An apparatus of feedback for a 4-antenna downlinkchannel in a Multiple Input Multiple Output (MIMO) system, comprising: adetection module, configured to detect a downlink multiple-antennachannel; a first determination module, configured to determine a firstcodeword in a first level codebook corresponding to the rank of Raccording to a long-term broadband channel characteristic estimated froma result of the detection, wherein any codeword in the first levelcodebook is four diagonal matrices, two same 2×C block matrices exist ona diagonal line, and C column vectors of the 2×C block matrix areselected from Q₁ discrete Fourier transform (DFT) beam vectors; afeedback module, configured to feed back an index of the first codeword;a second determination module, configured to determine a second codewordin a second level codebook corresponding to the rank of R according to ashort-term channel characteristic estimated from the result of thedetection and the first codeword, wherein any codeword in the secondlevel codebook is a 2C×R matrix, and each column of the 2C×R matrix isformed of one C×1 beam selection vector and one C×1 beam selectionvector comprising phase offset information; wherein the feedback moduleis further configured to feed back an index of the second codeword. 9.The apparatus according to claim 8, wherein a column vector of acodeword in the first level codebook comprises DFT beam vectors with anequal stride and DFT beam vectors orthogonal to each other, or comprisesDFT beam vectors with an equal stride but no DFT beam vectors orthogonalto each other.
 10. The apparatus according to claim 8, whereincorresponding to the rank of 1, a column vector of any codeword in thesecond level codebook is configured as selecting a same or different DFTbeam independently for each polarization, or configured as selecting asame DFT beam for each polarization.
 11. The apparatus according toclaim 8, wherein corresponding to the rank of 2, a column vector of anycodeword in the second level codebook is configured as selecting a sameor different DFT beam independently for each polarization and selectinga same DFT beam for each layer, or configured as selecting a same ordifferent DFT beam for each layer independently and selecting a same DFTbeam for each polarization, or configured as selecting a same ordifferent DFT beam independently for each polarization and selecting asame or different DFT beam for each layer independently, or configuredas selecting a same DFT beam for each polarization and selecting a sameDFT beam for each layer.
 12. The apparatus according to claim 8, whereina first level codebook corresponding to the rank of 3 or 4 is a propersubset of a first level codebook corresponding to the rank of 1 or 2.13. The apparatus according to claim 8, wherein corresponding to therank of 3 or 4, a column vector of the 2×C block matrix comprises DFTbeam vectors orthogonal to each other, and a column vector of anycodeword in the second level codebook is configured as selecting a sameor different DFT beam independently for each polarization, or configuredas selecting a same DFT beam for each polarization.
 14. (canceled)
 15. Auser equipment, comprising the apparatus of claim
 8. 16. A method foruse in a base station having 4 transmit antennas in a Multiple InputMultiple Output (MIMO) system, comprising: receiving a rank of downlinktransmission, an index of a first codeword in a first level codebook,and an index of a second codeword in a second level codebook fed back bya user equipment, wherein any codeword in the first level codebook isfour diagonal matrices, two same 2×C block matrices exist on a diagonalline, C column vectors of the 2×C block matrix are selected from Q₁discrete Fourier transform (DFT) beam vectors, any codeword in thesecond level codebook is a 2C×R matrix, and each column of the 2C×Rmatrix is formed of one C×1 beam selection vector and one C×1 beamselection vector comprising phase offset information; and determining adownlink channel characteristic according to the rank, the index of thefirst codeword, and the index of the second codeword. 17.-21. (canceled)22. An apparatus for use in a base station having 4 transmit antennas ina Multiple Input Multiple Output (MIMO) system, comprising: a receivingmodule, configured to receive a rank of downlink transmission, an indexof a first codeword in a first level codebook, and an index of a secondcodeword in a second level codebook fed back by a user equipment,wherein any codeword in the first level codebook is four diagonalmatrices, two same 2×C block matrices exist on a diagonal line, C columnvectors of the 2×C block matrix are selected from Q₁ discrete Fouriertransform (DFT) beam vectors, any codeword in the second level codebookis a 2C×R matrix, and each column of the 2C×R matrix is formed of oneC×1 beam selection vector and one C×1 beam selection vector comprisingphase offset information; and a channel characteristic determinationmodule, configured to determine a downlink channel characteristicaccording to the rank, the index of the first codeword, and the index ofthe second codeword.
 23. The apparatus according to claim 22, wherein acolumn vector of a codeword in the first level codebook comprises DFTbeam vectors with an equal stride and DFT beam vectors orthogonal toeach other, or comprises DFT beam vectors with an equal stride but noDFT beam vectors orthogonal to each other.
 24. The apparatus accordingto claim 22, wherein corresponding to the rank of 1, a column vector ofany codeword in the second level codebook is configured as selecting asame or different DFT beam independently for each polarization, orconfigured as selecting a same DFT beam for each polarization.
 25. Theapparatus according to claim 22, wherein corresponding to the rank of 2,a column vector of any codeword in the second level codebook isconfigured as selecting a same or different DFT beam independently foreach polarization and selecting a same DFT beam for each layer, orconfigured as selecting a same or different DFT beam for each layerindependently and selecting a same DFT beam for each polarization, orconfigured as selecting a same or different DFT beam independently foreach polarization and selecting a same or different DFT beam for eachlayer independently, or configured as selecting a same DFT beam for eachpolarization and selecting a same DFT beam for each layer.
 26. Theapparatus according to claim 22, wherein a first level codebookcorresponding to the rank of 3 or 4 is a proper subset of a first levelcodebook corresponding to the rank of 1 or
 2. 27. (canceled)
 28. A basestation equipment, comprising the apparatus of claim 22.